Terahertz lasers and amplifiers based on resonant optical phonon scattering to achieve population inversion

ABSTRACT

The present invention provides quantum cascade lasers and amplifier that operate in a frequency range of about 1 Terahertz to about 10 Terahertz. In one aspect, a quantum cascade laser of the invention includes a semiconductor heterostructure that provides a plurality of lasing modules connected in series. Each lasing module includes a plurality of quantum well structure that collectively generate at least an upper lasing state, a lower lasing state, and a relaxation state such that the upper and the lower lasing states are separated by an energy corresponding to an optical frequency in a range of about 1 to about 10 Terahertz. The lower lasing state is selectively depopulated via resonant LO-phonon scattering of electrons into the relaxation state.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under Contract No.PO#P927326 awarded by AFOSR, Contract No. NAG5-9080 awarded by NASA, andContract No. ECS-0217782 awarded by NSF. The government has certainrights in the invention.

BACKGROUND OF THE INVENTION

The present invention pertains generally to quantum cascade lasers(QCL), and more particularly, it relates to quantum cascade lasers thatoperate in the terahertz region of the electromagnetic spectrum.

The terahertz region (e.g., ˜1–10 THz, corresponding to a wavelengthλ=30–300 μm or a photon energy hω≈4–40 meV) of the electromagneticspectrum falls between microwave/millimeter and near-infrared/opticalfrequency ranges. Numerous coherent radiation sources have beendeveloped in the microwave/millimeter and near-infrared/opticalfrequency ranges. However, despite potential applications of terahertzradiation in a variety of different fields (e.g., spectroscopy inchemistry and biology, plasma diagnostics, remote atmospheric sensingand monitoring, and detection of bio- and chemical agents and explosivesfor security and military applications), coherent radiation sourcesoperating in the terahertz region remain scarce. The difficulties indeveloping such radiation sources can be appreciated by considering thatsemiconductor devices, such as, Gunn oscillators, or Schottky-diodefrequency multipliers, that utilize classical real-space chargetransport for generating radiation exhibit power levels that decrease asthe fourth power of radiation frequency

$( \frac{1}{f^{4}} )$as the radiation frequency (f) increases above 1 THz. Further, theradiation frequencies obtained from photonic or quantum electronicdevices, such as laser diodes, are limited by the semiconductor energybandgap of such devices, which is typically higher than 10 THz even fornarrow gap lead-salt materials. Thus, the frequency range below 10 THzis not accessible by employing conventional semiconductor laser diodes.

Some unipolar quantum well semiconductor lasers operating in themid-infrared portion of the electromagnetic spectrum are known. Forexample, electrically pumped unipolar intersubband transition lasers,commonly known also as quantum cascade lasers, operating at a wavelengthof 4 microns were developed at Bell Laboratories in 1994. Since then,major improvements in power levels, operating temperatures, andfrequency characteristics have been made for mid-infrared QCLs.

In contrast to such developments of QCL's in the mid-infrared range, thedevelopment of terahertz quantum cascade lasers in a frequency rangebelow 10 THz has been considerably more challenging. In particular,small separation of lasing energy levels (about 10 meV), coupled withdifficulties associated with mode confinement, at these frequenciescontribute to challenges in developing such lasers.

Hence, there is a need for coherent terahertz radiation sources,particularly, coherent sources that generate radiation in a frequencyrange of about 1 to about 10 THz.

There is also a need for efficient methods for mode confinement in suchterahertz lasers.

SUMMARY OF THE INVENTION

In one aspect, the present invention provides terahertz quantum cascadelasers that operate in a frequency range of about 1 to about 10Terahertz. A quantum cascade laser of the invention can include anactive region generally formed as a semiconductor heterostructure thatprovides a plurality of lasing modules connected in series. Each lasingmodule includes at least an upper lasing state, a lower lasing state anda relaxation state. The upper and the lower lasing states are separatedin energy by a value corresponding to an optical frequency in a range ofabout 1 to about 10 Terahertz. Hence, optical radiative transitionsbetween the upper lasing state and the lower lasing state generateradiation having a frequency in a range of about 1 to about 10Terahertz.

Applicants have discovered that a highly selective and very fastdepopulation of the lower lasing state can be achieved by employingresonant LO-phonon scattering of electrons populating the lower lasingstate into the relaxation state. For example, the rate of depopulationscattering can be higher than 10¹² s⁻¹ (a lifetime of the lower lasingstate being less than 1 psec), and further it can be largely insensitiveto operating temperature. This feature advantageously facilitatesgeneration of a population inversion between the upper and the lowerlasing states. More particularly, the energy separation of the lowerlasing state and the relaxation state is designed to allow resonantLO-phonon scattering of electrons from the lower lasing state into therelaxation state. In other words, this energy separation isapproximately equal to the energy of at least one LO-phonon mode of theheterostructure.

As is known in the art, the rate of radiative transitions between thelasing states and the non-radiative transitions between the lasingstates and the relaxation state are determined not only by energyseparation between these states, but also by the shapes of thewavefunctions associated with these states. In a terahertz laser of theinvention, the wavefunction of the lower lasing state of each lasingmodule has a substantial coupling to that of the relaxation state whilethe corresponding coupling between the upper lasing state and therelaxation state is substantially diminished. This can be accomplished,for example, by placing another state (e.g., level 3 in FIG. 5) atresonance with the lower lasing state. This other state, which can beprimarily located in the same well as the relaxation state, couplesstrongly with the relaxation state. When this other state (level 3) andthe lower lasing state (e.g., level 4 in FIG. 5) are brought intoresonance through a bias voltage, the lower lasing state becomesstrongly coupled to the relaxation state as well. However, the upperlasing state (e.g., level 5 in FIG. 5) is far from resonance and onlyweakly coupled to the relaxation state. As a result, despite a smallenergy separation between the upper and the lower lasing states relativeto their energy separation from the relaxation state, the lower lasingstate exhibits non-radiative transition rate into the relaxation statethat is considerably faster (e.g., by a factor of ˜10) than thecorresponding transition rate of the upper lasing state. For example, aratio of the non-radiative transition rate of the lower lasing stateinto the relaxation state relative to a corresponding rate of the upperlasing state can be in a range of about 5 to about 10. These factorsenhance the non-radiative lifetime of the upper lasing state relative tothat of the lower lasing state, thereby facilitating generation of apopulation inversion between these two states. For example, the lifetimeof the upper lasing state can be approximately 10 times longer than thatof the lower lasing state. In addition, the wavefunctions of the upperand lower lasing states are designed such that their coupling issufficiently strong to allow fast radiative transitions between theupper and the lower lasing states, thereby enhancing lasing efficiency.

In one aspect, a quantum cascade laser of the invention includeselectrical contacts that can apply a bias voltage across theheterostructure forming the active region of the laser. The bias voltagecauses a shift in the energy levels of various states of the lasingmodules such that a relaxation state of each module is in substantialresonance with an upper lasing state of an adjacent module to allowresonant tunneling of electrons from the relaxation state into theadjacent upper lasing state.

An active region of a quantum cascade laser of the invention asdescribed above can be formed, for example, as a cascaded series ofalternating layers of GaAs and Al_(x)Ga_(y)As sandwiched between anupper contact layer and a lower contact layer, wherein the aluminumconcentration (x) can range from about 15% to about 30%, and the galliumconcentration (y) can range from about 65% to about 80%. Those havingordinary skill in the art will appreciate it that other concentrationranges may also be suitable for the practice of the invention. Thecontact layers can be, for example, heavily doped (e.g., with Si dopantsthat provide n-type doping) GaAs layers (e.g., a doping level of about3×10¹⁸ cm⁻³). The heterostructure and the contact layers can be formedon a semi-insulating substrate, e.g., a semi-insulating GaAs layer.

In a related aspect, a quantum cascade laser of the invention caninclude a waveguide coupled to the active region for confining selectedlasing modes. Such a waveguide can be formed, for example, as a metalliclayer and a heavily doped semiconductor layer, for example, a heavilydoped GaAs layer, that provides mode confinement via surface plasmons.More preferably, the waveguide is formed of two metallic layers, forexample, two gold layers, between which the active region is disposed.

A terahertz quantum cascade laser of the invention has been demonstratedto operate at temperatures up to about 137 K (e.g., at temperatures in arange of about 5K to 137 K). Generally, the invention provides theopportunity for fabricating quantum cascade lasers that can operate ateven higher temperature (for example, at room temperature)

In another aspect, the invention provides an amplifier capable ofoperating in a range of about 1 to about 10 THz that includes anamplification region formed as a heterostructure that provides an upperand a lower amplification states and a relaxation state. The loweramplification state exhibits a non-radiative coupling to the relaxationstate via resonant LO-phonon scattering. The amplifier includes an inputport for optically coupling incoming radiation to the amplificationregion to generate an amplified signal that can be extracted from theamplifier via an output port.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective schematic view of a quantum laser according tothe teachings of the invention,

FIG. 2 is a cross-sectional view of the laser of FIG. 1 illustrating aheterostructure forming the laser's active region,

FIGS. 3A–3E schematically illustrate various steps in an exemplaryfabrication method for generating a double-sided metal waveguide for usein a terahertz laser according to one embodiment of the invention,

FIG. 4A depicts graphs of calculated mode profile and the real part ofdielectric constant in various layers of a quantum cascade laseraccording to one embodiment of the invention at a wavelength of 100microns and utilizing a waveguide formed of a metal layer and a heavilydoped semiconductor layer for mode confinement,

FIG. 4B depicts graphs of calculated mode profile and the real part ofdielectric constant in various layers of a quantum cascade laseraccording to another embodiment of the invention at a wavelength of 100microns and utilizing a double-sided metal waveguide for modeconfinement,

FIG. 5 illustrates an exemplary calculated conduction band profile oftwo lasing modules of a quantum cascade laser fabricated in accordancewith the teachings of the invention,

FIG. 6 is a schematic diagram of an experimental measurement system fortesting proto-type quantum cascade lasers formed in accordance with theteachings of the invention,

FIG. 7 illustrates a plurality of measured emission spectra of anexemplary quantum cascade laser formed in accordance with the teachingsof the invention,

FIG. 8 is a perspective view of a quantum cascade laser according to oneembodiment of the invention, which utilizes surface plasmon for modeconfinement,

FIG. 9 presents graphs illustrating bias voltage versus injectedcurrent, as well as optical power as a function of current, in aproto-type laser formed in accordance with the embodiment of FIG. 8,

FIG. 10 illustrates a plurality of measured emission spectra obtainedfrom a proto-type laser formed in accordance with the embodiment of FIG.8, and

FIG. 11 is a schematic perspective view of a terahertz amplifierfabricated in accordance with the teachings of the invention.

DETAILED DESCRIPTION

With reference to FIGS. 1 and 2, an exemplary quantum cascade laser 10according to one exemplary embodiment of the invention includes anactive lasing region 12 formed as a heterostructure on a GaAs substrate(for example, an n+ GaAs substrate) 14. The active region 12, which canhave a thickness in a range of about 3 microns to about 10 microns (inthis exemplary embodiment, the active region has a thickness of about 10microns), includes a plurality of cascaded nominally identical repeatlasing modules 16, which are coupled in series. The number of the lasingmodules can range, for example, from about 100 to about 200. In thisexemplary embodiment, the number of lasing modules is selected to be175.

Each lasing module can be formed as a GaAs/Al_(0.15)Ga_(0.85)Asheterostructure. For example, as shown in FIG. 1, in this embodiment,each lasing module, which has an approximate thickness of 600 angstroms,is formed as a stack of alternating Al_(0.15)Ga_(0.85)As and GaAs layershaving the illustrated thicknesses. The heterostructure of each lasingmodule provides four quantum wells that collectively generate lasing andrelaxation states, as described in more detail below. More particularly,each GaAs layer sandwiched between two Al_(0.15)Ga_(0.85)As barrierlayers functions as a two-dimensional quantum well.

The term “quantum well” is known in the art. To the extent that adefinition may be needed, a “quantum well,” as used herein, refers to agenerally planar semiconductor region, having a selected composition,that is sandwiched between semiconductor regions (typically referred toas barrier layers) having a different composition, commonly selected toexhibit a larger bandgap energy than that of the composition of thequantum well layer. The spacing between the barrier layers, andconsequently the thickness of the quantum well layer, are selected suchthat charge carriers (e.g., electrons) residing in the quantum welllayer exhibit quantum effects in a direction perpendicular to the layer(e.g., they can be characterized by discrete quantized energy states).

Two parallel metallic layers 18 and 20, formed of gold in thisembodiment, provide a double sided metal waveguide for confining thelasing modes of the laser 10. The double-sided metal waveguide tightlyconfines the radiation field, thus yielding a confinement factor closeto unity, as discussed in more detail below. Further, as shown in FIG.1, the upper and lower metallic layers 18 and 20 can be utilized toapply a selected bias voltage across the active region to cause shiftingof the energy levels, and injection of electrons into the active region,as discussed in more detail below.

Two heavily doped GaAs upper and lower contact layers 22 and 24 areemployed to provide low-resistive contact between the metal layers andthe semiconductor active region. In this exemplary embodiment, the uppercontact layer 22, which has a thickness of about 60 nm has a dopinglevel of about n=5×10¹⁸ cm⁻³, and the lower contact layer 24, which hasa thickness of about 100 mm, has a doping level of about n=3×10¹⁸ cm⁻³.Those having ordinary skill in the art will appreciate that other dopinglevels can also be utilized.

The operation of a terahertz quantum cascade laser of the invention,such as the above exemplary laser 10, will be discussed in more detailbelow. However, briefly, in operation, electrons injected into theactive region populate an upper lasing state of a lasing module, andgenerate lasing radiation via optical transitions to a lower lasingstate of the module. The energy separation of the upper and the lowerlasing states corresponds to a frequency in a range of about 1 to about10 THz (a wavelength range of about 30 to 300 microns), and hence thelasing radiation has a frequency in this range. The lower lasing stateis depopulated via resonant LO-phonon scattering into a relaxationstate. The applied bias voltage causes the relaxation state to be inenergetic proximity of an upper lasing state of an adjacent lasingmodule. This allows resonant tunneling of electrons from the relaxationstate into the upper lasing state of an adjacent module in a cascadingfashion.

The active region 12 can be formed as a heterostructure by employing,for example, molecular beam epitaxy (MBE), chemical vapor deposition(CVD), or any other suitable technique known in the art. A lowtemperature wafer bonding technique, described in detail below, can beemployed to generate the double-sided metal waveguide.

With reference to FIGS. 3A–3E, an exemplary fabrication method forgenerating the metallic layers 18 and 20 employs a low temperature metalwafer bonding technique followed by substrate removal. Moreparticularly, with reference to FIG. 3A, in an initial step, a wafer 26containing a multi quantum well (MQW) structure 28 according to theteachings of the invention, formed on a GaAs substrate, is coated with alayer of titanium (Ti) (e.g., a thickness of about 20 nm) and a layer 30of gold (e.g., a thickness of about 1000 nm). Further, a receptor wafer32 is prepared by depositing successive layers of palladium (Pd),germanium (Ge), palladium (Pd), indium (In), and gold (Au) on a doped n+GaAs substrate 34. The Pd/Ge/Pd multi-layer advantageously improveselectrical contact to the receptor layer while the topmost gold layerminimizes oxidation of the indium layer.

With reference to FIG. 3B, the two wafers 26 and 32 are bonded togetherand the GaAs layer 29 is removed. For example, in this exemplaryembodiment, wafer pieces having a cross-sectional area of about 1 cm⁻²were cleaved and bonded by maintaining stacked wafers at a temperatureof about 250 C on a hot plate for a time duration of about 10 minuteswhile pressure was applied to the stack. Care was taken to maintainalignment of the crystal axes of the two wafers. Bonding takes place asthe indium layer melts, wets the surface to fill in any crevices, andthen diffuses into the gold layer to reactively form a variety of In—Aualloys. When the layer thicknesses are properly selected, the indiumlayer is entirely consumed, and the bonding remains robust up to theeutectic temperature (about 450 C) of the In—Au alloys. The GaAssubstrate 29 can be first mechanically lapped and then chemically etchedin NH₄OH:H₂O₂ to cause its removal. This selective etch can be stoppedat a Al_(0.5)Ga_(0.5)As etch stop layer 36, which can be subsequentlyremoved by employing HF acid.

With reference to FIG. 3C, subsequently, a lithographic mask 38 isapplied to the upper surface of the active region by employing knowntechniques to pattern the surface so as to provide an opening in acentral portion of the surface while covering the remainder of thesurface. As shown in FIG. 3D, gold is then deposited over the mask toform a gold layer 40 in direct contact with the active region and a goldlayer 42 over the lithographic mask. The lithographic mask and the goldlayer are then lifted off the surface by dissolving the mask in anappropriate solvent. With reference to FIG. 3E, reactive ion etching,for example, electron cyclotron resonance reactive ion etching in aBCl₃:N₂ gas mixture, can then be utilized to etch the portions of theactive region that are not covered by the upper gold layer so as togenerate vertical sidewall profiles.

The use of double-sided metal waveguides in quantum cascade lasersoperating in a range of about 1 THz to about 10 THz according to theteachings of the invention considerably enhances mode confinement insuch lasers, for example, relative to employing semi-insulating surfaceplasmon waveguides. For example, FIGS. 4A and 4B illustrate calculatedmode intensities (solid lines) and the real part of dielectric constants(ε) (dashed lines) at a wavelength of 100 microns in two quantum cascadelasers utilizing, respectively, a waveguide formed of one metallic layerand a semi insulating surface plasmon layer and a double sided metalwaveguide. The calculations were based on Drude model for free electronsin various layers. A scattering time of 0.5 picoseconds (ps) wasemployed for electrons in the lightly doped active region whilescattering times of 0.1 ps and 0.05 ps were utilized, respectively, forelectrons in a heavily doped n+ GaAs substrate layers and in goldlayers.

With continued reference to FIGS. 4A and 4B, the double-sided metalwaveguide provides a mode confinement factor close to unity (Γ=0.98),which is considerably larger than the mode confinement factor (Γ=0.164)provided by the surface plasmon waveguide. In particular, while themodal intensity in the laser structure having a surface plasmonwaveguide extends considerably into the GaAs substrate (FIG. 4A), themodal intensity in the structure having a double-sided metal waveguideis confined almost completely within the active region. Thus, thestructure having a double-sided metal waveguide exhibits a much lowerfacet loss

$( \frac{\alpha_{m}}{\Gamma} )$than the other structure, although the waveguide losses

$( \frac{\alpha_{w}}{\Gamma} )$exhibited by the two structures are comparable. Hence, utilizing adouble-sided metal waveguide at a frequency in a range of about 1 THz toabout 10 THz for mode confinement results in a much lower total cavityloss, thus allowing obtaining lasing radiation in structures fabricatedbased on this mode confinement scheme in the terahertz region of theelectromagnetic spectrum.

In addition to providing enhanced mode confinement, a double-sided metalwaveguide according to the teachings of the invention can also beemployed as a microstrip transmission line that is compatible withintegrated circuits. This feature can allow THz QCL devices based onsuch metal waveguide structures to be readily integrated with othersemiconductor devices and circuits.

The operation of a quantum cascade laser fabricated in accordance withthe teachings of the invention can be better understood by reference toFIG. 5 that schematically illustrates a calculated conduction bandprofile corresponding to the above exemplary lasing structure 10 of thepresent exemplary embodiment. Although only two adjacent lasing modulesare illustrated in FIG. 5, those having ordinary skill in the art willappreciate that this exemplary illustration is applicable to othermodules in the active region. This exemplary conduction band profiledepicts the energy levels of two adjacent lasing modules 44 and 46 uponapplication of a bias voltage of 65 mV/module to the active region. Forexample, the module 44, which includes four quantum wells 48, 50, 52,and 54, includes quantum states E5, E4, E3, E2, and E1. The adjacentlasing module 46 includes similar energy states, albeit shifted inenergy relative to the corresponding states in the module 44 as a resultof application of the bias voltage. Each energy state is characterizedby a wavefunction whose modulus is indicative of the probabilitydistribution of an electron residing in that state.

The states E5 and E4 form, respectively, an upper lasing state and alower lasing state of the module 44. In preferred embodiments of theinvention, the upper lasing state E5 is separated from the lower lasingstate E4 by an energy corresponding to an optical transition frequencyin a range of about 1 to about 10 Terahertz (THz) between the two lasingstates. For example, in this exemplary embodiment, the energy separationbetween the upper and the lower lasing states E5 and E4 can be selectedto be 13.9 millielectronvolts (meV), which corresponds to an opticaltransition frequency of 3.38 THz (i.e., a wavelength (λ) of 88.8microns).

The states E1 and E2 form a relaxation doublet into which electronsresiding in the lasing states can transition, primarily viaphonon-assisted non-radiative processes. As described in more detailbelow, the transition rate of electrons from the lower lasing state intothe relaxation states is substantially faster than a correspondingtransition rate from the upper lasing state into the relaxation state.This difference in transition rates advantageously facilitatesgeneration of a population inversion between the two lasing states. Moreparticularly, at the design bias voltage, the state E3 is brought intoresonance with the lower lasing state E4 with a small anticrossing gap,for example, a gap of about 5 meV for a bias voltage of 64 meV in thisexemplary embodiment. The state E3 exhibits a fast relaxation rate viaresonant LO-phonon scattering into the relaxation double E1/E2. Thisallows fast resonant LO-phonon scattering from the lower lasing state E4into the relaxation states to selectively depopulate the lower lasingstate, thereby facilitating generation of a population inversion betweenthe lasing states.

A calculation of LO-phonon scattering rates for the exemplary lasingstructure 10, performed by employing bulk GaAs phonon modes (a goodapproximation for structures with low aluminum content), indicates aphonon scattering rate of about 1.8×10¹² s⁻¹ (corresponding to ascattering time of ˜0.55 ps) from the lower lasing state into therelaxation doublet (a lifetime of the lower lasing state into therelaxation doublet being τ₄ (2,1)=0.55 ps). Further, assuming a fullycoherent tunneling process between levels E3 and E4, electron-electronscattering from the lower lasing state E4 into the state E3, which has ashort lifetime (e.g., about 0.46 ps for transitions into the relaxationdoublet), can cause further depopulation of the lower lasing state.

In contrast, the non-radiative relaxation of the upper lasing state E5into the states E4 and E3 is suppressed at low temperatures as emissionof LO-phonons that can cause such transitions is energetically forbidden(i.e., the energy separation of E5 and E4 can be less than phononenergy). Further, as described in more detail below, the wavefunction ofthe the upper lasing state and and those of the relaxation states aredesigned to exhibit poor coupling with one another, thus minimizingnon-radiative transitions from the upper lasing state into therelaxation state. Hence, the lifetime of the upper lasing state issubstantially longer than that the lifetime of the lower lasing state.For example, in this exemplary embodiment, the lifetime of the lowerlasing state τ₄ is about 0.5 ps whereas the lifetime of the upper lasingstate τ₅ is about 7 ps. It should be understood that the abovecalculated numerical values are presented only for further elucidationof salient features of the invention, and are not intended to provideactual values of relaxation rates in all quantum cascade lasersfabricated in accordance with the teachings of the invention.

As is known in the art, the rate of a radiative transition between thelasing states, and the rates of non-radiative transitions between eachof the lasing states and the relaxation states are determined, in part,by the shapes of the wavefunctions of these states. In other words, thespatial probability of electron distribution in these states play a rolein establishing these transition rates. The selective depopulation ofthe lower lasing state via resonant LO-phonon scattering can be perhapsbetter understood by noting that in quantum cascade lasers of theinvention, the wavefunctions of the lasing states and the relaxationstate (or states) are designed such that the lower lasing state has asubstantial coupling to that of the relaxation state while thecorresponding coupling between the upper lasing state and the relaxationstate is minimized. Moreover, the energy separation of the lower lasingstate and the relaxation state (or states) is designed to allow resonantLO-phonon scattering from the lower lasing state into the relaxationstate. In addition, the wavefunctions of the two lasing states aredesigned to exhibit a sufficiently strong coupling that allows efficientradiative transition between these two states.

For example, in this exemplary embodiment, the wavefunction of the upperlasing state E5 has a substantial amplitude in the quantum wells 48 and50 while exhibiting a substantially diminished amplitude in the quantumwells 52 and 54. In contrast, the wavefunction of the lower lasing stateE4 exhibits robust amplitudes in the quantum wells 48 and 50, as well asin quantum well 52, but it has a much lower, amplitude in the quantumwell 54. The relaxation states E1 and E2 exhibit very low amplitudes inthe quantum wells 48 and 50, but have substantial amplitudes in thequantum wells 52 and 54. Further, the quantum state E3 has a substantialamplitude in the quantum well 52, and a somewhat lower amplitude in thequantum well 48. A coupling between two wavefunctions as used herein, isa measure of an spatial extent over which both wavefunctions havenon-vanishing (or substantial) amplitudes. For example, a couplingbetween two wavefunctions can be obtained by integrating a product ofthe two wavefunctions over a selected spatial extent. Alternatively, acoupling between two wavefunctions can be obtained by calculating theexpectation value of an operator (e.g., dipole moment operator) betweenthe two wavefunctions. A review of the above wavefunctions reveals thatthe coupling between the wavefunction of the lower lasing state andthose of the relaxation states is much more enhanced relative to asimilar coupling between the wavefunction of the upper lasing state andthose of the relaxation states. More specifically, the wavefunction ofthe lower lasing state, and that of the state E3 that is in resonancewith the lower lasing state, and those of the relaxation states havesubstantial amplitudes in the quantum well 52, whereas the wavefunctionof the upper lasing state has approximately vanishing values in thequantum wells 52 and 54 in which the wavefunctions of the relaxationstates peak. Hence, the rate of non-radiative transitions from the lowerlasing state into the relaxation state is much higher (e.g. about 10times larger) than a corresponding rate associated with the upper lasingstate.

Further, there exists a good coupling between the wavefunctions of theupper and the lower lasing states because both wavefunctions exhibitsubstantial amplitudes in the quantum wells 48 and 50. In other words, aradiative transition between the lasing states E5 and E4 is spatiallyvertical, i.e., it involves electronic transitions within the samequantum well rather than between adjacent quantum wells, thus yielding alarge oscillator strength f₅₄, e.g., an oscillator strength of about0.96 in this embodiment. A large oscillator strength advantageouslyallows efficient lasing between these two states.

With continued reference to FIG. 5, the relaxation states E1′ and E2′ ofthe adjacent lasing module 46 are shifted in energy relative to thecorresponding relaxation states of the lasing module 44, as a result ofapplication of the bias voltage, so as to be in energetic proximity ofthe upper lasing state E5. The small energy separation between thestates E1′ and E2′ and the upper lasing state E5 allows transfer ofelectrons, via resonant tunneling, from the states E1′ and E2′ into theupper lasing state E5, thereby providing a mechanism for populating theupper lasing state E5.

During operation of the laser, electrons are injected into the lasingstructure 10, and are transferred from the relaxation state(s) of onelasing module to the upper lasing state of an adjacent lasing module ina cascading fashion. The transfer of electrons into the upper lasingstate, coupled with selective depopulation of the lower lasing state viaresonant LO-phonon relaxation, generates a population inversion betweenthe upper and the lower lasing states, as described above. The directuse of LO-phonons in quantum cascade lasers of the invention fordepopulation of the lower lasing state offers at least two distinctadvantages. First, when a relaxation state (collector state) isseparated from the lower lasing state by at least E_(LO) (longitudinaloptical (LO) phonon energy), depopulation can be extremely fast, and itdoes not depend much on temperature or electron distribution. Second,the large energy separation between the lower lasing state and therelaxation state inhibits thermal backfilling of the lower lasing state.These properties advantageously allow generating lasers in the terahertzregion that operate at relatively high temperatures. For example, asdescribed in more detail below, Applicants have observed lasing inproto-type lasers fabricated in accordance with the teachings of theinvention up to an operating temperature of about 137 K.

Although the operation of a quantum cascade laser of the invention wasdescribed above with reference to five quantum states in each lasingmodule, it should be understood that a quantum cascade laser of theinvention can function with a minimum of three quantum states in eachlasing module such that two of the states form an upper lasing state anda lower lasing state, and third state functions as a relaxation statefor depopulating the lower lasing state via resonant LO-phononscattering.

To illustrate the efficacy of the teachings of the invention forgenerating quantum cascade lasers that operate in a frequency range ofabout 1 to about 10 THz, a prototype quantum cascade laser, whichoperates at a frequency of about 3.8 THz (λ≈79 μm) was constructed andtested. Lasing was observed up to an operating temperature of 137 K.This proto-type lasing structure includes an active region formed of 178cascaded lasing modules, generated over an insulating GaAs substrate byemploying molecular bean epitaxy. Further, cladding and contact layerswere grown in a manner described. The thickness of the undopedAl_(0.5)Ga_(0.5)As etch-stop layer in this exemplary prototype structurewas selected to be 0.3 microns. Further, the lower n⁺ GaAs contact layerhas a thickness of 0.8 microns and is doped at 3×10¹⁸ cm⁻³. Moreover,the intra-injector barrier has a thickness of 30 angstroms resulting inan anticrossing gap of 5 meV between the injector (relaxation) states(E1 and E2). A tighter injector doublet provides a more selectiveinjection into the upper lasing state of an adjacent module. Adouble-sided metal waveguide was employed for mode confinement.

A standard experimental set-up, shown in FIG. 6, was utilized formeasurements of the prototype device's lasing emission. A device undertest 56 was mounted on a heat sink 58 that was cooled by a coolant tolower the device's temperature to a desired value. A plurality of 200 nsbias pulses were applied to the device to elicit lasing emissiontherefrom. The lasing emission was coupled to an input of a Fouriertransform spectrometer 60 operating at 0.125 cm⁻¹ resolution, and wasdetected by a Ge:Ga photodetector 62 coupled to an output of thespectrometer. The output of the detector was routed to an input of alock-in amplifier 64 whose reference input was supplied with the pulsetrain. The output of the lock-in amplifier provided emission spectra ofthe device under test.

FIG. 7 illustrates observed lasing emission spectra at differenttemperatures obtained from the above proto-type device. The observedfrequency shift at different temperatures is believed to be due tomode-hopping caused by the shift of the gain curve at slightly differentbias points, and not to temperature tuning. The spontaneous emissionlinewidth is measured to be about 6 meV (about 1.5 THz). Without beinglimited to any theory, this broad linewidth, which is considerablydifferent than a Lorentzian linewidth, is likely due to a non-uniformalignment of different lasing modules.

Although preferred embodiments of the invention employ a double-sidedmetal waveguide for mode confinement, in some other embodiments of theinvention, mode confinement can be achieved by sandwiching an activeregion between a top metal layer and a heavily doped semiconductor(e.g., GaAs) bottom layer that provides a certain degree of modeconfinement via surface plasmon effect. By way of example, FIG. 8schematically depicts an exemplary quantum cascade laser 66 inaccordance with one embodiment of the invention that utilizes surfaceplasmon for mode confinement. The exemplary laser 66 includes an activeregion 68 formed as a stack of a plurality of lasing modules, asdescribed above. An upper metallic layer 70 and a heavily doped contactlayer 72, for example, a contact layer having a thickness of about 0.8microns and doped at 3×10¹⁸ cm⁻³ cooperatively provide confinement ofthe lasing modes. As the plasma frequency associated with this lowercontact layer lies above the frequency of interest, a waveguide isformed between the upper metallic contact and the surface plasmonsassociated with the quasimetallic lower contact layer. Moreparticularly, in this exemplary embodiment, non-alloyed ohmic contactscomposed of Ti/Au are deposited on a low temperature grown n++ GaAs topcontact layer. Wet etching is then utilized to pattern a few hundredmicrons wide (e.g., 200 μm) ridges 74. Ni/Ge/Au alloyed contacts canthen be made to exposed portions of the contact layer 72 adjacent theridges to allow, together with the metallic layer 70, application of abias voltage across the active region.

As described in more detail below, a proto-type device that utilizes asurface plasmon waveguide was fabricated according to the aboveembodiment of the invention. More particularly, this prototype deviceincluded an active region formed as a GaAs/Al_(0.15)Ga_(0.85)Asheterostructure fabricated on a 600 micron thick semi-insulating GaAswafer by employing molecular beam epitaxy. The waveguide and ridges forproviding ohmic contact with the lower contact layer were fabricated asdescribed above. A Fabry-Perot cavity was formed by cleaving thestructure into a 1.18 mm long bar, and the back facet was coated byevaporating Ti/Au over silicon nitride. The device was then mountedridge side up on a copper cold finger in a helium cryostat for testing.An measurement system, such as the system shown in above FIG. 6, wasthen employed to obtain the presented emission data.

The device was tested at a plurality of temperatures in a range of about5 K to about 87 K. The testing was performed by applying 200 ns longelectrical pulses repeated at a rate of 1 kHz (corresponding to a 0.02%duty cycle) to the device. A Ge:Ga photodetector was utilized to measurethe intensity of lasing emission. Further, a pyroelectric detectorhaving a 2-mm diameter detecting element onto which an incoming beam canbe focused by employing cone optics was utilized to calibratemeasurement of absolute power. However, because the collectionefficiency was considerably less than unity, the reported uncorrectedpower levels underestimate the actual emitted power levels. As discussedin more detail below, lasing at a frequency of about 3.4 THz wasobserved even at a relatively high temperature of 87 K.

FIG. 9 presents observed laser emission power at a plurality ofoperating temperatures as a function of applied current in thisprototype device, together with bias voltage as a function of current.At a temperature of 5K, a threshold current density (J_(th)) of 806A/cm², and a peak power of ˜14 mW were observed. At an operatingtemperature of 87 K, J_(th) increased to 904 A/cm², and the peakobserved power decreased to approximately ˜4 mW. An insert 76 in FIG. 1illustrates the dependence of the threshold current on operatingtemperature.

FIG. 10 illustrates a typical lasing emission spectrum of this prototypelaser measured at an operating temperature of 78 K. The center frequencyof this emission spectrum occurs at a frequency of 3.38 THzcorresponding to a wavelength of 88.6 microns (μm). An insert 78provided in FIG. 10 illustrates a plurality of emission spectra obtainedat the same temperature at different values of the injection currentdensity. The observed lasing emission is largely single mode at lowerinjection currents, for example, in a range in which the slope ofpower-current relation is positive (i.e., current less than about 4.8A). At high injection currents, e.g., currents above about 4.8 A, thelasing emission power decreases as injection current increases. Withoutbeing limited to any particular theory, such decrease of emission poweris expected to be due to a misalignment of injector states relative tothe corresponding upper lasing states receiving electrons from theinjector states. Consequently, the emission spectra at high currentsexhibit increasingly multi-mode behavior with shifts to higherfrequencies. This blue shift of the frequency is believed to be due tothe Stark shift of the intersubband transitions. A measured mode spacingat a temperature of 5 K is approximately 0.51 cm⁻¹, which corresponds toan effective mode index (n_(eff)) of 3.8±0.1. The individual modes arecontinuously redshifted by approximately 0.16 cm⁻² (i.e., 4.8 GHz) asthe operating temperature is increased from about 5 K to about 78 K.

It should be understood that the data presented above in connection withvarious proto-type lasers fabricated according to the teachings of theinvention are provided only for illustrative purposes, and are notintended to necessarily indicate optimal operating characteristics, suchas output power or spectral lineshape, of a quantum cascade laser formedaccording to the teachings of the invention. Moreover, it should beunderstood that the teachings of the invention can be practiced togenerate quantum cascade lasers that operate at frequencies other thanthose of the above prototype devices, and generally, in a frequencyrange of about 1 to about 10 THz.

The teachings of invention are not limited to fabricating quantumcascade lasers in a frequency range of about 1 to about 10 THz. Inparticular, the teachings of the invention can be applied to fabricateamplifiers in this wavelength range. By way of example, FIG. 11schematically illustrates an amplifier 80 according to one embodiment ofthe invention that operates in a range of about 1 to about 10 THz. Theexemplary amplifier 80 includes an active region 82 formed as aheterostructure, for example, alternating GaAs and Al_(0.15)Ga_(0.85)Aslayers, in accordance with the teachings of the invention, as describedabove. Radiation in a frequency range of 1 to 10 THz can be coupled tothe active region via an input port 84. Amplified radiation can exit theactive region via an output port 86. Input and output facets 88 and 90are cleaved so as to suppress self oscillation of the amplifyingstructure due to reflections at these surfaces. Further, a waveguide 92,for example, a double-sided metal waveguide, confines the radiation tothe amplification region.

Those having ordinary skill in the art will appreciate that variousmodifications can be made to the above embodiments without departingfrom the scope of the invention.

1. A quantum cascade laser, comprising a semiconductor heterostructureproviding a plurality of lasing modules connected in series, each lasingmodule comprising a plurality of quantum well structures collectivelygenerating at least an upper lasing state, a lower lasing state, and arelaxation state such that said upper and lower lasing states areseparated by an energy corresponding to an optical frequency in a rangeof about 1 to about 10 Terahertz, and such that a radiative lasingtransition between said upper lasing state and said lower state isspatially vertical, and wherein electrons populating said lower lasingstate exhibit a non-radiative relaxation via resonant emission ofLO-phonon into said relaxation state and wherein said resonant LO-phononemission selectively depopulates the lower lasing state such that aratio of a lifetime of said upper lasing state relative to a lifetime ofsaid lower lasing state is at least sbout
 5. 2. The quantum cascadelaser of claim 1, wherein said non-radiative relaxation of the lowerlasing state into the relaxation state at a selected operatingtemperature of said laser is faster than a corresponding relaxation rateof said upper lasing state into said lower lasing state, and whereinsaid resonant LO-phonon emission selectively depopulates the lowerlasing state such that a ratio of a lifetime of said upper lasing staterelative to lifetime of said lower lasing state is at least about
 10. 3.The quantum cascade laser of claim 1, wherein said laser generateslasing radiation at an operating temperature above about 87 K.
 4. Thequantum cascade laser of claim 1, wherein the laser operates in a pulsemode.
 5. The quantum cascade laser of claim 1, further comprising anelectrical contact for applying a bias voltage across said semiconductorheterostructure.
 6. The quantum cascade laser of claim 5, wherein saidapplied bias voltage causes a relaxation state of each lasing module tobe in substantial resonance with an upper lasing state of an adjacentmodule to allow resonant tunneling of electrons therebetween.
 7. Thequantum cascade laser of claim 6, wherein electrons populating an upperlasing state of each lasing module exhibit a vertical optical transitioninto a lower lasing state of said module.
 8. The quantum cascade laserof claim 5, wherein in each of said modules, said quantum wells generatea fourth state in substantial resonance with said lower lasing stateupon application of said bias voltage.
 9. The quantum cascade laser ofclaim 8, wherein electrons populating said fourth state exhibitrelaxation via resonant LO-phonon scattering into said relaxation state.10. The quantum cascade laser of claim 1, wherein in each of said lasingmodules, said relaxation state is characterized by a wavefunctionexhibiting substantial amplitude in a first one of said quantum wells,said upper lasing state is characterized by a wavefunction substantiallyconcentrated in quantum wells other than said first quantum well, andsaid lower lasing state exhibiting sufficient amplitude in said firstquantum well so as to cause a substantial phonon coupling between saidlower lasing state and said relaxation state.
 11. The quantum cascadelaser of claim 10, wherein for each of said lasing modules, both of saidupper and said lower lasing states exhibit substantial amplitudes in atleast one of said quantum wells so as to allow a vertical opticaltransition between said upper and lower lasing states.
 12. The quantumcascade laser of claim 1, further comprising an upper contact layer anda lower contact layer between which said semiconductor heterostructureis disposed.
 13. The quantum cascade laser of claim 12, wherein saidcontact layers are formed of a heavily doped GaAs.
 14. The quantumcascade laser of claim 13, wherein said contact layers are formed ofGaAs having a doping level of about 3×10¹⁸ cm⁻³.
 15. The quantum cascadelaser of claim 1, wherein said semiconductor heterostructure is formedas a stack of alternating GaAs and Al_(0.15)Ga_(0.85)As layers.
 16. Thequantum cascade laser of claim 15, wherein said heterostructure has athickness in a range of about 1 to about 10 microns.
 17. The quantumcascade laser of claim 1, further comprising a waveguide coupled to saidsemiconductor heterostructure for confining selected lasing modes ofsaid laser.
 18. The quantum cascade laser of claim 17, wherein saidwaveguide is formed of a metallic layer and a heavily dopedsemiconductor layer between which said semiconductor heterostructure issandwiched.
 19. The quantum cascade laser of claim 18, wherein saidwaveguide is formed of two metallic layers between which saidsemiconductor heterostructure is sandwiched.
 20. The quantum cascadelaser of claim 1, wherein a number of said lasing modules of saidheterostructure range from about 100 to about
 200. 21. The quantumcascade laser of claim 1, further comprising a semiconductor substrateon which said heterostructure is formed.
 22. The quantum cascade laserof claim 21, wherein said substrate comprises a semi-insulating GaAssubstrate.
 23. A quantum cascade laser, comprising a semiconductorheterostructure providing a plurality of lasing modules connected inseries, each lasing module comprising a plurality of quantum wellstructures collectively generating at least an upper lasing state, alower lasing state, and a relaxation state such that said upper andlower lasing states are separated by an energy corresponding to anoptical frequency in a range of about 1 to about 10 Terahertz and suchthat a radiative lasing transition between said upper lasing state andsaid lower lasing state is spatially vertical, and wherein electronspopulating said lower lasing state exhibit a non-radiative relaxationvia resonant emission of LO-phonon into said relaxation state andwherein said resonant LO-phonon emission selectively depopulates thelower lasing state such that a ratio of a lifetime of said uppedr lasingstate relative to a lifetime of said lower lasing state is at leastabout 5, wherein the laser generates lasing radiation at an operatingtemperature above 130 K.
 24. A terahertz amplifier, comprising anamplification structure formed as a semiconductor heterostructureincluding a plurality of amplification modules connected in series, eachmodule comprising a plurality of quantum wells cooperatively generatingan upper and lower amplification states and a relaxation state, saidupper and lower states being separated in energy by a valuecorresponding to an optical frequency in a range of about 1 to about 10Terahertz, said lower state being separated in energy from saidrelaxation state by a value substantially equal to an energy of at leastone LO-phonon mode of said heterostructure such that electrons in saidlower state exhibit relaxation into said relaxation state via resonantLO-phonon scattering, an input port for coupling an input signal in afrequency range of about 1 to about 10 Terahertz into said amplificationstructure to generate an amplified signal, and an output port forextracting said amplified signal from said amplification structurewherein said upper and lower amplification states exhibit a spatiallyvertical radiative transition and wherein a ratio of lifetime of saidupper amplification state relative to that of said lower amplificationstate is at least about
 5. 25. A quantum cascade laser, comprising asemiconductor substrate, a heterostructure formed on said semiconductorsubstrate, said heterostructure comprising a plurality of lasing modulesconnected in series, each of said modules comprising: a plurality ofquantum well structures collectively generating an upper lasing state, alower lasing state, and a relaxation state, said upper and said lowerlasing states having an energy separation corresponding to an opticalfrequency in a range of about 1 THz to about 10 THz, wherein a verticaltransition between the upper lasing state and the lower lasing stategenerates lasing radiation and resonant LO-phonon scattering ofelectrons from said lower lasing state into said relaxation statedepopulates said lower lasing state to facilitate generation of apopulation inversion between the upper and the lower lasing states.wherein a rate of relaxation of said lower lasing state into therelaxation state is at least about 5 times higher than a correspondingrate associated with the upper lasing state.
 26. The quantum cascadelaser of claim 25, wherein said LO-phonon scattering of electrons fromsaid lower lasing state into said relaxation state exhibits a rate in arange of about 0.1 to about 0.6 picoseconds.
 27. A quantum cascadelaser, comprising a semiconductor heterostructure providing a pluralityof lasing modules connected in series, each lasing module comprising aplurality of quantum well structures collectively generating at least anupper lasing state, a lower lasing state, and a relaxation state suchthat said upper and lower lasing states are separated by an energycorresponding to an optical frequency in a range of about 1 to about 10Terahertz, such that a radiative lasing transition between said upperlasing state and said lower lasing state is spatially vertical, andelectrons populating said lower lasing state exhibit a non-radiativerelaxation via resonant emission of LO-phonon into said relaxationstate, and wherein a rate of relaxation of said lower lasing state intothe relaxation state is at least about 5 times higher than acorresponding rate associated with the upper lasing state, and the lasergenerates lasing radiation at operating temperatures above about 87 K.28. A quantum cascade laser, comprising a semiconductor heterostructureproviding a plurality of lasing modules connected in series, each lasingmodule comprising a plurality of quantum well structures collectivelygenerating at least an upper lasing state, a lower lasing state, and arelaxation state such that said upper and lower lasing states areseparated by an energy corresponding to an optical frequency in a rangeof about 1 to about 10 Terahertz, said upper and lower lasing statesexhibiting a spatially vertical radiative transition with an oscillatorstrength of about unity, wherein electrons populating said lower lasingstate exhibit a non-radiative relaxation via resonant emission ofLO-phonon into said relaxation state and wherein said resonant LO-phononemission selectively depopulates the lower lasing state such that ratioof a lifetime of said upper lasing state relative to a lifetime of saidlower lasing state is at least about 5.